You can safely update the AAT's FW to a new release of the same major version i.e. update from v4.1 to v4.4
What IS more problematic is updating to a new major release as there's a good chance that stuff will break.
I think the best option is to export a few courses and test them in the FW to see what will break; then go from there. If you want to play it safe and create a new instance of the AAT rather than update your existing one... well that would make sense.
From having updated quite a few (FW-only courses) I can say that your major problem going from an older version to v4 will be with any plugins that extend or have dependencies upon the functionality of the core components, in particular because of all the changes we made to split them properly into model/view. The (rarely used) pointGMCQ component currently doesn't work with v4 for that reason.
Aside from that the accessibility functionality was the biggest recent change; that's documented here. As a general rule, implement accessibility is actually now much simpler.
Otherwise it generally is quite straightforward and most plugins seem to work fine. Ones to keep an eye on are those that haven't been touched the the developer in years; check the github repo to see.